On the Impact of Regularization Variation on Localized Multiple Kernel Learning

Micro, Small, and Medium Enterprises’ Business Vulnerability Cluster in Indonesia: An Analysis Using Optimized Fuzzy Geodemographic Clustering

The COVID-19 pandemic has caused effects in many sectors, including in businesses and enterprises. The most vulnerable businesses to COVID-19 are micro, small, and medium enterprises (MSMEs). Therefore, this paper aims to analyze the business vulnerability of MSMEs in Indonesia using the fuzzy spatial clustering approach. The fuzzy spatial clustering approach had been implemented to analyze the social vulnerability to natural hazards in Indonesia. Moreover, this study proposes the Flower Pollination Algorithm (FPA) to optimize the Fuzzy Geographically Weighted Clustering (FGWC) in order to cluster the business vulnerability in Indonesia. We performed the data analysis with the dataset from Indonesia’s national socioeconomic and labor force survey (SUSENAS and SAKERNAS). We first compared the performance of FPA with traditional FGWC, as well as several known optimization algorithms in FGWC such as Artificial Bee Colony, Intelligent Firefly Algorithm, Particle Swarm Optimization, and Gravitational Search Algorithm. Our results showed that FPAFGWC has the best performance in optimizing the FGWC clustering result in the business vulnerability context. We found that almost all of the regions in Indonesia outside Java Island have vulnerable businesses. Meanwhile, in most of Java Island, particularly the JABODETABEK area that is the national economic backbone, businesses are not vulnerable. Based on the results of the study, we provide the recommendation to handle the gap between the number of micro and small enterprises (MSMEs) in Indonesia.

SVRG-MKL: A Fast and Scalable Multiple Kernel Learning Solution for Features Combination in Multi-Class Classification Problems

In this paper, we present a novel strategy to combine a set of compact descriptors to leverage an associated recognition task. We formulate the problem from a multiple kernel learning (MKL) perspective and solve it following a stochastic variance reduced gradient (SVRG) approach to address its scalability, currently an open issue. MKL models are ideal candidates to jointly learn the optimal combination of features along with its associated predictor. However, they are unable to scale beyond a dozen thousand of samples due to high computational and memory requirements, which severely limits their applicability. We propose SVRG-MKL, an MKL solution with inherent scalability properties that can optimally combine multiple descriptors involving millions of samples. Our solution takes place directly in the primal to avoid Gram matrices computation and memory allocation, whereas the optimization is performed with a proposed algorithm of linear complexity and hence computationally efficient. Our proposition builds upon recent progress in SVRG with the distinction that each kernel is treated differently during optimization, which results in a faster convergence than applying off-the-shelf SVRG into MKL. Extensive experimental validation conducted on several benchmarking data sets confirms a higher accuracy and a significant speedup of our solution. Our technique can be extended to other MKL problems, including visual search and transfer learning, as well as other formulations, such as group-sensitive (GMKL) and localized MKL (LMKL) in convex settings.

Multiple Kernel Clustering With Neighbor-Kernel Subspace Segmentation

Multiple kernel clustering (MKC) has been intensively studied during the last few decades. Even though they demonstrate promising clustering performance in various applications, existing MKC algorithms do not sufficiently consider the intrinsic neighborhood structure among base kernels, which could adversely affect the clustering performance. In this paper, we propose a simple yet effective neighbor-kernel-based MKC algorithm to address this issue. Specifically, we first define a neighbor kernel, which can be utilized to preserve the block diagonal structure and strengthen the robustness against noise and outliers among base kernels. After that, we linearly combine these base neighbor kernels to extract a consensus affinity matrix through an exact-rank-constrained subspace segmentation. The naturally possessed block diagonal structure of neighbor kernels better serves the subsequent subspace segmentation, and in turn, the extracted shared structure is further refined through subspace segmentation based on the combined neighbor kernels. In this manner, the above two learning processes can be seamlessly coupled and negotiate with each other to achieve better clustering. Furthermore, we carefully design an efficient iterative optimization algorithm with proven convergence to address the resultant optimization problem. As a by-product, we reveal an interesting insight into the exact-rank constraint in ridge regression by careful theoretical analysis: it back-projects the solution of the unconstrained counterpart to its principal components. Comprehensive experiments have been conducted on several benchmark data sets, and the results demonstrate the effectiveness of the proposed algorithm.

Early Expression Detection via Online Multi-Instance Learning With Nonlinear Extension

Video-based facial expression recognition has received substantial attention over the past decade, while early expression detection (EED) is still a relatively new and challenging problem. The goal of EED is to identify an expression as quickly as possible after the expression starts and before it ends. This timely ability has many potential applications, ranging from human-computer interaction to security. The max-margin early event detector (MMED) is a well-known ranking model for early event detection. It can achieve competitive EED performance but suffers from several critical limitations: 1) MMED lacks flexibility in extracting useful information for segment comparison, which leads to poor performance in exploring the ranking relation between segment pairs; 2) the training process is slow due to the large number of constraints, and the memory requirement is also usually hard to satisfy; and 3) MMED is linear in nature, and hence may not be appropriate for data in a nonlinear feature space. To overcome these limitations, we propose an online multi-instance learning (MIL) framework for EED. In particular, the MIL technique is first introduced to generalize MMED, resulting in the proposed MIL-based EED (MIED), which is more general and flexible than MMED, since various instance construction and combination strategies can be adopted. To accelerate the training process, we reformulate MIED in the online setting and develop online multi-instance learning framework for EED (OMIED). To further exploit the nonlinear structure of the data distribution, we incorporate the kernel methods in OMIED, which results in the proposed online kernel multi-instance learning for early expression detection. Experiments on two popular and one challenging video-based expression data sets demonstrate both the efficiency and effectiveness of the proposed methods.